A student attempts to solve the following compound inequality 2−3x>8 OR 5x−2>13. If the solution is incorrect, where did the student first go wrong and why?
1. Solve 2−3x>8. x<−2
2. Solve 5x−2>13. x>3
3. Recombine the solutions. −2<x<3(1 point)
Responses
In step 2, the solution is incorrect. It should be x<3 because when you add a negative number, you have to switch the direction of the inequality.
In step 2, the solution is incorrect. It should be x less than 3 because when you add a negative number, you have to switch the direction of the inequality.
The solution to the first branch is incorrect because the direction of the inequality was switched when it should not have been.
The solution to the first branch is incorrect because the direction of the inequality was switched when it should not have been.
In step 3, the recombination of the two branches of the compound inequality is incorrect. They are merged as if they are an AND inequality, when they should be merged as an OR inequality.
In step 3, the recombination of the two branches of the compound inequality is incorrect. They are merged as if they are an AND inequality, when they should be merged as an OR inequality.
No mistake has been made.
In step 2, the solution is incorrect. It should be x<3 because when you add a negative number, you have to switch the direction of the inequality.
In step 3, the recombination of the two branches of the compound inequality is incorrect. They are merged as if they are an AND inequality, when they should be merged as an OR inequality.
Therefore, the correct response is: In step 2, the solution is incorrect. It should be x<3 because when you add a negative number, you have to switch the direction of the inequality.